Generalization properties of finite size polynomial Support Vector Machines

Details Generalization properties of finite size polynomial Support Vector Machines Generalization properties of finite size polynomial Support Vector Machines

2000-02-04

arxiv.org/abs/cond-mat/0002071v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, 7 figures

Scientific paper

10.1103/PhysRevE.62.7092

The learning properties of finite size polynomial Support Vector Machines are analyzed in the case of realizable classification tasks. The normalization of the high order features acts as a squeezing factor, introducing a strong anisotropy in the patterns distribution in feature space. As a function of the training set size, the corresponding generalization error presents a crossover, more or less abrupt depending on the distribution's anisotropy and on the task to be learned, between a fast-decreasing and a slowly decreasing regime. This behaviour corresponds to the stepwise decrease found by Dietrich et al.[Phys. Rev. Lett. 82 (1999) 2975-2978] in the thermodynamic limit. The theoretical results are in excellent agreement with the numerical simulations.

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